Let the G.P. be :       a , ar , ar² , ar³ , ............ ar^{2n - 1}       where 'r' is the common ratio

Given :   S1  =  a + ar² + ar⁴ + ........... + ar^{2n - 2}   =  a( (r² )ⁿ  -  1 ) / r² - 1

               S2  =  ar + ar³ + ar⁵ + ............. + ar^{2n - 1}   =  ar ( (r²)ⁿ  -  1 ) / r² - 1

Therefore : S2 / S1  =  r